Q. No.The quantity of heat required to take a system from \(\mathrm{A}\) to \(\mathrm{C}\) through the process \(\mathrm{ABC}\) is \(20\) cal. The quantity of heat required to go from \(\mathrm{A}\) to \(\mathrm{C}\) directly is:
1. \(20\) cal
2. \(24.2\) cal
3. \(21\) cal
4. \(23\) cal
The internal energy of a gas is given by \(U=2pV.\) The gas expands from \(100\) cc to \(200\) cc against a constant pressure of \(10^{5}\) Pa. The heat absorbed by the gas is:
1. \(10\) J
2. \(20\) J
3. \(30\) J
4. \(40\) J
The ratio \(C_P/C_V=1.5\) for a certain ideal gas. The gas is taken at an initial pressure of \(2\) kPa and compressed suddenly to \(\dfrac14\) of its initial volume. The final pressure is:
1. \(\dfrac12\) kPa
2. \(4\) kPa
3. \(8\) kPa
4. \(16\) kPa
An ideal gas is enclosed in a volume by means of a piston-cylinder arrangement as shown in the adjacent diagram. The piston as well as the walls of the cylinder are non-conducting. The cross-sectional area of the piston is \(A.\) Gravity \(g\) is acting downward. A small block of mass \(m\) is placed on top of the piston. There is no atmospheric pressure outside. An amount of thermal energy \(\Delta Q\) is slowly supplied to the gas, and its temperature rises. Then, the gas:
| 1. | expands continuously, making the volume infinite. |
| 2. | first expands and then contracts slightly. |
| 3. | expands and then reaches a steady-state. |
| 4. | expands and then contracts to return to its initial volume. |
In a reversible process, the change in internal energy \(U\) of an ideal gas \((C_P/C_V=\gamma)\) is zero, while the volume increases from \(V\) to \(2V\). If the initial pressure is \(P\), the final pressure will be:
| 1. | \(2P\) | 2. | \(\dfrac P2\) |
| 3. | \(P\) | 4. | \(\dfrac{P}{2^\gamma}\) |
| 1. | \(300\) K | 2. | \(\dfrac{300}{2^{5/3}}\) K |
| 3. | \(\dfrac{300}{2^{2/3}}\) K | 4. | \(600\) K |
| 1. | \(U_0\mathrm{ln}(2)\) | 2. | \(\dfrac12U_0~\mathrm{ln}(2)\) |
| 3. | \(\dfrac13U_0~\mathrm{ln}(2)\) | 4. | \(\dfrac23U_0~\mathrm{ln}(2)\) |
| 1. | \(\dfrac {V}{T}\) = constant | 2. | \(\dfrac {V^2}{T}\) = constant |
| 3. | \(\dfrac {T^2}{V}\) = constant | 4. | \(TV^2\) = constant |
| 1. | increases by \(1.5\%\) |
| 2. | decreases by \(1.5\%\) |
| 3. | increases by \(\frac13\%\) |
| 4. | increases by \(\frac23\%\) |
where \(dQ\) is the heat supplied to the gas and \(T\) is the temperature of the gas. The integral is evaluated over the entire cycle. The value of the integral \(I\) is:
| 1. | zero |
| 2. | negative |
| 3. | positive |
| 4. | non-negative(positive or zero) |
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